research-article

Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication

Authors:

Toniann Pitassi,

Thomas WatsonAuthors Info & Claims

ITCS '15: Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science

Pages 113 - 122

https://doi.org/10.1145/2688073.2688074

Published: 11 January 2015 Publication History

Abstract

We study whether information complexity can be used to attack the long-standing open problem of proving lower bounds against Arthur{Merlin (AM) communication protocols. Our starting point is to show that|in contrast to plain randomized communication complexity|every boolean function admits an AM communication protocol where on each yes- input, the distribution of Merlin's proof leaks no information about the input and moreover, this proof is unique for each outcome of Arthur's randomness. We posit that these two properties of zero information leakage and unambiguity on yes-inputs are interesting in their own right and worthy of investigation as new avenues toward AM.

Zero-information protocols (ZAM). Our basic ZAM protocol uses exponential communication for some functions, and this raises the question of whether more efficient protocols exist. We prove that all functions in the classical space-bounded complexity classes NL and L have polynomial-communication ZAM protocols. We also prove that ZAM complexity is lower bounded by conondeterministic communication complexity.

Unambiguous protocols (UAM). Our most technically substantial result is a (n) lower bound on the UAM complexity of the NP-complete set-intersection function; the proof uses information complexity arguments in a new, indirect way and overcomes the \zero-information barrier" described above. We also prove that in general, UAM complexity is lower bounded by the classic discrepancy bound, and we give evidence that it is not generally lower bounded by the classic corruption bound.

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Index Terms

Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes

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cover image ACM Conferences

ITCS '15: Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science

January 2015

404 pages

ISBN:9781450333337

DOI:10.1145/2688073

Program Chair:
Tim Roughgarden
Stanford University

Copyright © 2015 ACM.

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Published: 11 January 2015

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ITCS '15 Paper Acceptance Rate 45 of 159 submissions, 28%;

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Cited By

Gur TLiu YRothblum R(2021)An Exponential Separation Between MA and AM Proofs of Proximitycomputational complexity10.1007/s00037-021-00212-330:2Online publication date: 18-Aug-2021
https://doi.org/10.1007/s00037-021-00212-3
Applebaum BRaykov P(2018)On the Relationship Between Statistical Zero-Knowledge and Statistical Randomized Encodingscomputational complexity10.1007/s00037-018-0170-xOnline publication date: 20-Aug-2018
https://doi.org/10.1007/s00037-018-0170-x
Applebaum BRaykov P(2017)From Private Simultaneous Messages to Zero-Information Arthur---Merlin Protocols and BackJournal of Cryptology10.1007/s00145-016-9239-330:4(961-988)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s00145-016-9239-3
Applebaum BArkis BRaykov PVasudevan P(2017)Conditional Disclosure of Secrets: Amplification, Closure, Amortization, Lower-Bounds, and SeparationsAdvances in Cryptology – CRYPTO 201710.1007/978-3-319-63688-7_24(727-757)Online publication date: 29-Jul-2017
https://doi.org/10.1007/978-3-319-63688-7_24
Applebaum BRaykov P(2016)On the Relationship Between Statistical Zero-Knowledge and Statistical Randomized EncodingsProceedings, Part III, of the 36th Annual International Cryptology Conference on Advances in Cryptology --- CRYPTO 2016 - Volume 981610.1007/978-3-662-53015-3_16(449-477)Online publication date: 14-Aug-2016
https://dl.acm.org/doi/10.1007/978-3-662-53015-3_16
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Applebaum BRaykov P(2015)From Private Simultaneous Messages to Zero-Information Arthur-Merlin Protocols and BackTheory of Cryptography10.1007/978-3-662-49099-0_3(65-82)Online publication date: 24-Dec-2015
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